Lecture 1.4 Limit involving Infinity - Chapter 1 Functions...

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Chapter 1: Functions, Limits and Continuity Lecture 4: Limits at Infinity and Infinite Limits By: Prof. Phan Quoc Khanh
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Outline of Chapter 1 1. Real Numbers, Real Line and Cartesian Coordinates 2. Functions and Graphs 3. Limits of Functions 4. Limits at Infinity and Infinite Limits 5. Continuity 6. Continuous Functions on Closed Finite Intervals 11/14/2014 Prof. Phan Quoc Khanh 2
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Limit at Infinity We say that f(x) approaches the limit L as x approaches infinity, and we write lim ( ) , if 0, 0 such that if , then belongs to domain of and | ( ) | x f x L R x R x f f x L ®¥ = " > > > - <
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Limit at Negative Infinity We say that f(x) approaches the limit L as x approaches negative infinity, and we write lim ( ) , if 0, 0 such that if , then belongs to domain of and | ( ) | x f x L K x K x f f x L ®-¥ = " > < < - <
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Example Show that 1 lim 0 Solution: Given 0. For 0 we have 1 1 1 1 0 , provided | | 1 lim 0 x x x x x R x x x x ®¥ ®¥ = > > - = = < > = Þ =
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Limits at Infinity For all n > 0, lim x ®¥ 1 x n = lim x ®-¥ 1 x n = 0 Ex.
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